积级数

Periodic signals which are neither absolutely integrable nor square integrable over an infinite interval, can be considered to have Fourier transforms if impulse functions are permitted in the transform.

若在变换过程中可以使用冲激函数，那么，在一个无限区间内，既不绝对可积，又不具备平方可积的周期信号也可以认为具有傅立叶级数。

We did our best to get the optimal methods to make the liquid more atomize, and established a model for gas-liquid mass and heat transfer process of cross-flow RPB.

根据气液两相流在多级离心加速雾化条件下流体的动量与质量方程，分析研究液体的雾化程度、液滴粒径、运动速度与方向、停留时间等，研究液相多级分散的级数、分散方式以及离心力场强度对气液相界面积、传质系数以及气相流阻的影响关系及其规律性，探讨沿旋转床径向使液体均匀雾化的最佳方法，建立旋转床中气液两相的运动与传质数学模型。

Based on the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation , the non-symmetrical banding solutions to the circular plate under thermal boundary conditions are gained by the Fourier series and convolution formulae.

根据双调和方程边值问题的边界积分公式和自然边界积分方程，利用傅立叶级数及卷积的几个公式，求得了相应变温边界条件下非对称载荷圆板的弯曲解，从实践上证明了此方法的可行性。

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

We study the relations among MS, QMDS, RBVS, AMDS, GBVS and NBVS. Finally. we improve some classic results in Fourier analysis such as uniform convergence, L~1 convergence, L~p-integrability, strong approximation of continuous functions et al., by applying this new condition.

我们研究了MS，QMDS，RBVS，AMDS，GBVS和NBVS等不同数列之间的关系，在此基础上，我们给出了NBV条件在研究三角级数的一致收敛性、L~1收敛性、L~p可积性、连续函数的强逼近等Fourier分析经典问题上的应用，对一些经典的结论作了推广。

A combinatorial identity is obtained:=:~z 2r扟32-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time.

第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式：第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

According to our teaching practice,effective applications of some relative calculus background knowledge in teaching are given,such as introduction of real number ,Newton-Leibniz s formula,principle of integrability,meaning of infinite series.

结合教学实践，讨论了实数的引入，Newton-Leibniz公式，无穷级数，函数的可积性准则这几个相关的微积分背景知识在教学中的有效运用。

On the basis of classical lamination theory and large deflection hypotheses of plate, the equilibrium and compatibility equations of simply supported composite laminated plates were obtained. The nonlinear partial differential equations are transformed into the ordinary differential equations of Kronecker tensor product by series expansion and solved numerically by the fourth-order Runge-Kutta method.

基於经典的层合板理论及板的大挠度基本假设，得到四边简支层合板的非线性运动方程及变形协调方程；用级数展开把非线性偏微分方程组化为易於求解的Kronecker张量积形式的二阶常微分方程组，并由四阶Runge-Kutta法数值求解。

Firstly, the Signal Noise Ratio characteristic of matched filter despread symbol and the distribution of coherent phase estimation error are derived. Secondly, the exact integration formula of BER for fading channel is presented, moreover, by using the Maclaurin series expansion of MPSK conditional Symbol Error Rate, the simplified BER approximations for BPSK and QPSK are derived over AWGN, Nakagami-m fading and Rayleigh fading channel.

首先推导了匹配滤波解扩符号的信噪比特性和相干相位估计误差的分布；然后给出了衰落信道中误比特率的精确积分式，并利用MPSK条件误符号率的麦克劳林级数形式，推导了AWGN，Nakagami-m衰落和瑞利衰落信道中BPSK，QPSK误比特率的简化逼近式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。